Int J Theor Phys (2018) 57:2124–2132
Truth Values of Quantum Phenomena
Received: 1 August 2017 / Accepted: 26 March 2018 / Published online: 2 April 2018
© Springer Science+Business Media, LLC, part of Springer Nature 2018
Abstract In the paper, the idea of describing not-yet-verified properties of quantum objects
with logical many-valuedness is scrutinized. As it is argued, to promote such an idea, the
following two foundational problems of many-valued quantum logic must be decided: the
problem of choosing a proper system of many-valued logic and the problem of the emer-
gence of bivalence from logical many-valuedness. Difficulties accompanying solutions of
these problems are discussed.
Keywords Quantum mechanics · Many-valued logics · Bivalence · Truth-functionality ·
Truth values · Quantum logic
1 Introducing Logical Many-Valuedness in Quantum Mechanics
The argument claiming that quantum theory could not be comprehended on the grounds of
classical two-valued logic is rather straightforward and goes like this.
Let us consider a typical quantum interference experiment where a quantum particle
being released from a source is absorbed by a screen after passing through a two-slit barrier.
Suppose that immediately behind that barrier are placed two which-way detectors able to
verify (e.g., by way of clicking) the particle’s passage through a corresponding slit. Let X
denote the proposition of the click of the detector placed behind slit 1 such that X
(denoted by “1”) if the detector clicks and X
is false (denoted by “0”) if the detector does
not. Let X
in an analogous manner denote the proposition of the signal from the detector
placed behind slit 2.
In the present paper, rather than being strictly restricted to spatially arranged slits, quantum interference is
considered generally for any set of perfectly distinguishable alternatives.
Ben-Gurion University of the Negev, Beersheba, Israel